Problem: Solve for $n$: $\frac{2-n}{n+1} + \frac{2n-4}{2-n} = 1$.
Explanation: Note that $\frac{2n-4}{2-n} = \frac{2(n-2)}{-(n-2)}=-2$.  From this, we can rewrite the given equation and solve: \begin{align*}
\frac{2-n}{n+1}-2&=1\\
\Rightarrow \qquad \frac{2-n}{n+1}&=3\\
\Rightarrow \qquad 2-n&=3n+3\\
\Rightarrow \qquad -1&=4n\\
\Rightarrow \qquad \boxed{-\frac{1}{4}}&=n
\end{align*}